Improved Calculation of Nonlinear Near-Bed Wave Orbital Velocity in Shallow Water: Validation against Laboratory and Field Data

A new parameterization for calculating the nonlinear near-bed wave orbital velocity in the shallow water was presented. The equations proposed by Isobe and Horikawa (1982) were modified in order to achieve more accurate predictions of the peak orbital velocities. Based on field data from Egmond Beach in the Netherlands, the correction coefficient and maximum skewness were determined as functions of the Ursell number. The obtained equations were validated against measurements from Egmond Beach, and with laboratory data from small-scale wave flume experiments at Delft University of Technology and from large-scale wave flume experiments at Delft Hydraulics. Inter-comparisons with other previously developed parameterizations were also carried out. The model simulations by the present study were in good agreement with the measurements and have been improved compared to the previous ones. For Egmond Beach, the root-mean-square errors for the peak onshore (uc) and offshore (ut) orbital velocities were approximately 21%. The relative biases were small, approximately 0.013 for uc and −0.068 for ut. The coefficient of determination was in the range between 0.64 and 0.68. For laboratory experiments, the root-mean-square errors in a range of 7.2%–24% for uc, and 7.9%–15% for ut.

Direct Measurements of Bed Shear Stress under Swash Flows on Steep Laboratory Slopes at Medium to Prototype Scales

Robust measurements of bed shear stress under wave runup flows are necessary to inform beachface sediment transport modelling. In this study, direct measurements of swash zone bed shear stress were obtained in medium and prototype-scale laboratory experiments on steep slopes. Peak shear stresses coincided with the arrival of uprush swash fronts and high-resolution measurement of swash surface profiles indicated a consistently seaward sloping swash surface with minimal evidence of a landward sloping swash front. The quadratic stress law was applied to back-calculate time-varying friction factors, which were observed to decrease with increasing Reynolds number on smooth slopes, consistent with theory for steady flows. Additionally, friction factors remained relatively constant throughout the swash cycle (except around flow reversal), with a variation of approximately ±20% from the mean value and with only small differences between uprush and backwash. Measured friction factors were observed to be larger than expected when plotted on the Moody or wave friction diagram for a given Reynolds number and relative roughness, consistent with previous field and laboratory studies at various scales.